We then consider the robustness of the AF state to defects by including values of tight-binding parameters that are constant within each layer (thus preserving translational invariance within each layer) but that vary randomly between layers. We compare disorder that preserves chiral symmetry (random values of the interlayer hoppings) with disorder that breaks chiral symmetry (random layer potentials). For weak disorder, we find that the mean band gap is diminished by chiral breaking disorder, but it is almost insensitive to chiral preserving disorder; this is similar to the behavior of gapless edge states in the non-interacting SSH model [1]}, [2]}, [3]}, [4]}, [5]}.
